Two points move evenly in one direction along a 60 m long circle. One of them makes a full revolution 5

Two points move evenly in one direction along a 60 m long circle. One of them makes a full revolution 5 seconds faster than the other. In this case, the points coincide every time after 1 minute. Determine the speed of movement of the points.

Suppose that the time it takes for the first point to complete a full circle is t.
In this case, since the speed of the second point is 5 seconds longer, we will write it as (t + 5).

The speed of the first point will be (60 / t). The speed of the second point is (60 / (t +5)).
Since the points intersect once every 1 minute – 60 seconds, the distance traveled by the first point during this time will be equal to (60 * 60) / t, and the second point – (60 * 60) / (t + 5).

Since the second point moves faster, it means that in 60 seconds it makes 1 more circle.

In this case, we get the following equation:
3600 / t = 3600 / (t + 5) + 60;

Expand the brackets and get:
t ^ 2 + 5 * t – 300 = 0.

We find the discriminant.
D = 5 ^ 2 – 4 * 1 * (-300) = 1225 = 35.
t1 = (-5 + 35) / 2 = 15 s.
t2 = (-5 – 35) / 2 = -20 s. (Inappropriate, because with a minus sign)

Substitute the resulting value into the equation.
V1 = 60/15 = 4 m / s. (The speed of the first point.)
V2 = 60 / (15 + 5) = 3 m / s. (Second point speed.)